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Optimal grid holey packings with block size 3 and 4

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Abstract

The notion of a grid holey packing (GHP) was first proposed for the construction of constant composite codes. For a GHP (k, 1; n ×  g) of type [w 1, . . . , w g ], where \({k = \sum_{j=1}^{g} w_j}\) , the fundamental problem is to determine the packing number N([w 1, . . . , w g ], 1; n ×  g), that is, the maximum number of blocks in such a GHP. In this paper we determine completely the values of N([w 1, . . . , w g ], 1; n ×  g) in the case of block size \({k\in \{3, 4\}}\) .

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Authors and Affiliations

  1. Department of Mathematics, Suzhou University, Suzhou, 215006, People’s Republic of China

    Bin Wen, Jianmin Wang & Jianxing Yin

  2. Department of Mathematics, Changshu Institute of Technology, Suzhou, 215500, People’s Republic of China

    Bin Wen

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  1. Bin Wen
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  2. Jianmin Wang
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  3. Jianxing Yin
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Correspondence to Jianmin Wang.

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Communicated by P. Wild.

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Wen, B., Wang, J. & Yin, J. Optimal grid holey packings with block size 3 and 4. Des. Codes Cryptogr. 52, 107–124 (2009). https://doi.org/10.1007/s10623-009-9270-6

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  • DOI: https://doi.org/10.1007/s10623-009-9270-6

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